A multilateral Bailey Lemma and multiple Andrews--Gordon identities

双边Bailey对与Rogers-Ramanujan型恒等式

Bilateral Bailey pairs and Rogers-Ramanujan type identities

本文利用q-二项式定理发现双边Bailey对，结合双边Bailey引理、链和格，统一推导出多种Rogers-Ramanujan型恒等式及Appell-Lerch、Andrews-Gordon和Hecke型级数恒等式。

来自Bailey格的截断theta级数

Truncated theta series from the Bailey lattice

本研究利用Bailey格推导奇基雅可比三重积级数的截断形式，得到多个经典theta级数的新截断式与分拆函数不等式，同时证实了相关分拆猜想并证明Merca强猜想在R=3S（S≥1）时成立。

Rogers–Ramanujan 型双边恒等式

Bilateral identities of the Rogers--Ramanujan type

本文利用解析方法建立一系列 Rogers–Ramanujan 型双边及多边恒等式，推广多项经典恒等式，并给出闭式求和。

关于安德鲁斯和沃纳亚尔的q恒等式的某些新结果

Some new results on Andrews' and Warnaar's q-identities

本文通过逆关系技术，推导出安德鲁斯q级数恒等式的广义形式及两个与部分theta函数求和恒等式相关的新型Bailey对和q恒等式。

Extensions of the well-poised and elliptic well-poised Bailey lemma

We establish a number of extensions of the well-poised Bailey lemma and elliptic well-poised Bailey lemma. As application we prove some new transformation formulae for basic and elliptic hypergeometric series, and embed some recent identities of Andrews, Berkovich and Spiridonov in a well-poised Bailey tree.

On Andrews--Warnaar's identities of partial theta functions

In this paper we set up a bivariate representation of partial theta functions which not only unifies some famous identities for partial theta functions due to Andrews and Warnaar, et al. but also unveils a new characteristic of such identities. As further applications, we establish a general form of Warnaar's identity and a general $q$--series transformation associated with Bailey pairs via the use of the power series expansion of partial theta functions.

Polynomial Identities Implying Capparelli's Partition Theorems

We propose and recursively prove polynomial identities which imply Capparelli's partition theorems. We also find perfect companions to the results of Andrews, and Alladi, Andrews and Gordon involving $q$-trinomial coefficients. We follow Kurşungöz's ideas to provide direct combinatorial interpretations of some of our expressions. We use of the trinomial analogue of Bailey's lemma to derive new identities. These identities relate triple sums and products. A couple of new Slater type identities are also noted.

Further results on Andrews--Yee's two identities for mock theta functions $ω(z;q)$ and $v(z;q)$

In this paper, by the method of comparing coefficients and the inverse technique, we establish the corresponding variate forms of two identities of Andrews and Yee for mock theta functions, as well as a few allied but unusual $q$-series identities. Among includes a new Bailey pair from which a product formula of two ${}_2ϕ_1$ series is derived. Further, we focus on two finite $q$-series summations arising from Andrews and Yee's mock theta function identities and expound some recurrence relations and transformation formulas behind them.

A new A_n extension of Ramanujan's 1-psi-1 summation with applications to multilateral A_n series

In this article, we derive some identities for multilateral basic hypergeometric series associated to the root system A_n. First, we apply Ismail's argument to an A_n q-binomial theorem of Milne and derive a new A_n generalization of Ramanujan's 1-psi-1 summation theorem. From this new A_n 1-psi-1 summation and from an A_n 1-psi-1 summation of Gustafson we deduce two lemmas for deriving simple A_n generalizations of bilateral basic hypergeometric series identities. These lemmas are closely related to the Macdonald identities for A_n. As samples for possible applications of these lemmas, we pro…

单位圆上的一族正交函数与一个新的双边矩阵逆

A family of orthogonal functions on the unit circle and a new multilateral matrix inverse

本文利用Bailey求和证明了特定级数构成单位圆上的正交函数族，并从Dougall求和提取出新的双边矩阵逆，结合Pfaff-Saalschütz求和推导了 $_3H_3$ 级数求和公式及其多变量扩展。

$\rm A_2$ Bailey树与$\rm A_2^{(1)}$ Rogers-Ramanujan型恒等式

An $\mathrm{A}_2$ Bailey tree and $\mathrm{A}_2^{(1)}$ Rogers-Ramanujan-type identities

本研究将$\rm A_2$ Bailey链拓展为四参数$\rm A_2$ Bailey树，以此证明了Kanade-Russell猜想、Andrews-Gordon恒等式的$\rm A_2^{(1)}$类比及更一般的Rogers-Selberg型恒等式，推广了已有结果。

An overpartition analogue of the Andrews-Göllnitz-Gordon theorem

In 1967, Andrews found a combinatorial generalization of the Göllnitz-Gordon theorem, which can be called the Andrews-Göllnitz-Gordon theorem. In 1980, Bressoud derived a multisum Rogers-Ramanujan-type identity, which can be considered as the generating function counterpart of the Andrews-Göllnitz-Gordon theorem. Lovejoy gave an overpartition analogue of the Andrews-Göllnitz-Gordon theorem for $i=k$. In this paper, we give an overpartition analogue of this theorem in the general case. By using Bailey's lemma and a change of base formula due to Bressoud, Ismail and Stanton, we obtain an overpar…

与Andrews奇偶性考虑相关的Andrews-Gordon型恒等式

An Andrews-Gordon Type Identity Related to Andrews' Parity Consideration

本文针对Rogers-Ramanujan-Gordon定理中k与a模2不同余的情况，利用Bailey引理导出Andrews-Gordon型恒等式，并通过格路峰值给出组合解释。

关于类型 $D_k$ 卡坦矩阵的纳姆求和恒等式

Nahm sum identities for Cartan matrices of type $D_k$

本文通过贝利配对理论重新证明了与类型 $D_k$ 卡坦矩阵相关的四个纳姆求和恒等式，并给出了其参数推广的两种不同证明。

双和罗格斯-拉曼努金型恒等式

Double-sum Rogers-Ramanujan type identities

本文通过Chebyshev多项式展开式与正交关系，推导出双和罗格斯-拉曼努金型恒等式，扩展了安德鲁斯、史、孙和姚等人的已有结果。

可分离整数划分类与Slater的列表 -- I

Separable integer partition classes and Slater's list -- I

本文利用Andrews的可分离整数划分理论，对Slater列表中的若干恒等式进行解析，提供自然的划分解释和参数化推广，并通过q-超几何变换推导出新的表达式。